The Analysis Of The Trust Region Algorithm

Optimization is an important branch of the operations research. Trust region method is a kind of effective algorithm for optimization. Many researchers in nonlinear optimization pay close attention to this method, because of its strong convergence and stability. In this paper, the BFGS correction formula is briefly improved on the basis of the previous work. The theoretical analysis on the improved algorithm convergence is presented.The main research contents are as follows:We first introduce main research work of this paper, including the contents of optimization theory, the background and research situation of the trust region method. In chapter 2, we introduce the elementary knowledge about this paper, including trust region algorithm convergence, line search method, mo-dified BFGS formula and so on.In chapter 3, we obtain a class of new BFGS trust region algorithm by two adjustable parameters, which results improve the previous conclusion of [21] and [53]and prove the global convergence of the algorithm under appropriate conditions.In chapter 4, we conclude a modified Quasi-Newton BFGS Rrust-Region algorithm with nonmonotone wolfe line search on the basis of the previous work,which results improve the previous conclusion. In this new algorithm, sequence is satisfied the quasi-Newt at each iteration and simultaneously satisfied positive-definite.We prove that the algorithms are global convergence under certain conditions.